Which of the following points is a solution of the inequality y < -|x|?
2 answers:
Answer: choice A only
(1,-2) is the only solution (from the list of choices)
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Explanation:
Let's go through each answer choice. We'll plug the coordinates in one at a time.
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Choice A has the point (1,-2) so x = 1 and y = -2 pair up together
y < -|x|
-2 < -|1|
-2 < -1
This is a true statement as -2 is to the left of -1 on the number line. So (1,-2) is one solution. Let's see if there are others.
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Choice B) plug in (x,y) = (1,-1)
y < -|x|
-1 < -|1|
-1 < -1
False. A number is not smaller than itself. So we can cross B off the list.
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Choice C) plug in (x,y) = (1,0)
y < -|x|
0 < -|1|
0 < -1
This is false because -1 is smaller than 0. Cross choice C off the list.
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Only choice A is a solution point for this inequality. If we were to graph the inequality, we would see only point A is in the shaded region while the other points are outside the shaded region.
The dashed boundary line does not count as the shaded region. This visually confirms why point B does not work.
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